Final answer:
The equation of the perpendicular line is y = -1/3x - 5/3.
Step-by-step explanation:
To find the equation of a line that is perpendicular to the line y=3x+3 and passes through the point (-5,0), we need to use the slope-intercept form of a line.
The slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.
Since we're looking for a line that is perpendicular, the slope of the new line will be the negative reciprocal of the slope of the given line.
The slope of y=3x+3 is 3, so the slope of the perpendicular line will be -1/3.
Now, to find the equation, we can use the point-slope form which is y-y1 = m(x-x1), where (x1, y1) is the given point. Substituting the values, we get: y-0 = -1/3(x-(-5)).
Simplifying, we get: y = -1/3x - 5/3.
Therefore, the equation of the line that is perpendicular to y=3x+3 and passes through (-5,0) is y = -1/3x - 5/3.